arXiv subjects

Kouji Kashiwa

Publications and source records attributed to Kouji Kashiwa.

At least 37 records · Page 2Linked to original sources

arXiv2021

Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses

The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure of zeros of the microscopic probability density function at the nonanalytic point. The average value of the Polyakov line can detect the structure, while the other thermodynamic quantities are not sensible to the structure in the zero-temperature limit. The effect of the imaginary quark chemical potential is also discussed. The imaginary part of the quark number density is very sensitive to the symmetry structure at the nonanalytical point. For a particular value of the imaginary quark number chemical potential, large quark number may be induced in the vicinity of the nonanalytical point.

hep-ph↗

arXiv2021

Anatomy of the dense QCD matter from canonical sectors

We investigate the nuclear and the quark matter at finite real chemical potential ($μ_\mathrm{R}$) and low temperature from the viewpoint of the canonical sectors constructed via the imaginary chemical potential region. Based on the large $N_\mathrm{c}$ estimation, where $N_\mathrm{c}$ is the number of color, we can discuss the confinement-deconfinement nature at finite $μ_\mathrm{R}$ from the canonical sectors. We found the expectation that the sharp change of canonical sectors at $μ_\mathrm{R} \sim M_\mathrm{B}/N_\mathrm{c}$, where $M_\mathrm{B}$ is the lowest baryon mass, is happen in the large $N_\mathrm{c}$ regime, and it is matched with the quarkyonic picture. In addition, we discussed the color superconductivity and the chiral properties from the structure of canonical sectors. Even in the present anatomy from the canonical sectors, we can have the suitable picture for the dense QCD matter.

hep-ph↗

arXiv2021

Persistent homology analysis for dense QCD effective model with heavy quarks

The isospin chemical potential region is known as the sign-problem free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic the dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it as QCD-like Potts model. The QCD-like Potts model does not have the sign problem, but we can expect that it shares some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential where the simple Metropolis algorithm can work, we perform the persistent homology analysis towards exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition.

hep-lat↗

arXiv2020

Path optimization for $U(1)$ gauge theory with complexified parameters

In this article, we apply the path optimization method to handle the complexified parameters in the 1+1 dimensional pure $U(1)$ gauge theory on the lattice. Complexified parameters make it possible to explore the Lee-Yang zeros which helps us to understand the phase structure and thus we consider the complex coupling constant with the path optimization method in the theory. We clarify the gauge fixing issue in the path optimization method; the gauge fixing helps to optimize the integration path effectively. With the gauge fixing, the path optimization method can treat the complex parameter and control the sign problem. It is the first step to directly tackle the Lee-Yang zero analysis of the gauge theory by using the path optimization method.

hep-lat↗

arXiv2020

Information theoretical view of QCD effective model with heavy quarks

To understand the phase transition phenomena, information theoretical approaches can pick up some important properties of the phenomena based on the probability distribution. In this paper, we show information theoretical aspects of the 3-dimensional 3-state Potts model with the external field which is corresponding to the QCD effective model with heavy quarks. The transfer mutual information which represents the information flow of two spin variables is numerically estimated based on the Markov-chain Monte-Carlo method. The transfer mutual information has the peak near the confinement-deconfinement transition, and it may be used to detect the precursors of the transition. Since the transfer mutual information still have the peak even if the Polyakov-loop changes continuously and smoothly, we may pick up some aspects of the confinement-deconfinement nature from the information flow properties. Particularly, the transfer mutual information shows the significantly different behavior below and above the Roberge-Weiss endpoint existed in the pure imaginary chemical potential region, which may indicate the system change by the confinement-deconfinement transition.

hep-ph↗

arXiv2020

Extension to Imaginary Chemical Potential in a Holographic Model

We extend a bottom up holographic model, which has been used in studying the color superconductivity in QCD, to the imaginary chemical potential ($μ_I$) region, and the phase diagram is studied on the $μ_I$-temperature (T) plane. The analysis is performed for the case of the probe approximation and for the background where the back reaction from the flavor fermions are taken into account. For both cases, we could find the expected Roberge-Weiss (RW) transitions. In the case of the back-reacted solution, a bound of the color number $N_c$ is found to produce the RW periodicity. It is given as $N_c\geq 1.2$. Furthermore, we could assure the validity of this extended model by comparing our result with the one of the lattice QCD near $μ_I=0$.

hep-th↗

arXiv2020

Persistent homology analysis of deconfinement transition in effective Polyakov-line model

The persistent homology analysis is applied to the effective Polyakov-line model on a rectangular lattice to investigate the confinement-deconfinement nature. The lattice data are mapped onto the complex Polyakov-line plane without taking the spatial average and then the plane is divided into three domains. This study is based on previous studies for the clusters and the percolation properties in lattice QCD, but the mathematical method of the analyses are different. The spatial distribution of the data in the individual domain is analyzed by using the persistent homology to obtain information of the multiscale structure of center clusters. In the confined phase, the data in the three domains show the same topological tendency characterized by the birth and death times of the holes which are estimated via the filtration of the alpha complexes in the data space, but do not in the deconfined phase. By considering the configuration averaged ratio of the birth and death times of holes, we can construct the nonlocal order-parameter of the confinement-deconfinement transition from the multiscale topological properties of center clusters.

hep-lat↗

arXiv2019

The path optimization for the sign problem of low dimensional QCD

The path optimization has been proposed to weaken the sign problem which appears in some field theories such as finite density QCD. In this method, we optimize the integration path in complex plain to enhance the average phase factor. In this study, we discuss the application of this method to low dimensional QCD as a first step of finite density QCD.

hep-lat↗

arXiv2019

Evading the model sign problem in the PNJL model with repulsive vector-type interaction via path optimization

We discuss the sign problem in the Polyakov loop extended Nambu--Jona-Lasinio model with repulsive vector-type interaction by using the path optimization method. In this model, both of the Polyakov loop and the vector-type interaction cause the model sign problem, and several prescriptions have been utilized even in the mean field treatment. In the path optimization method, integration variables are complexified and the integration path (manifold) is optimized to evade the sign problem, or equivalently to enhance the average phase factor. Within the homogeneous field ansatz, the path is optimized by using the feedforward neural network. We find that the assumptions adopted in previous works, $\mathrm{Re}\,A_8 \simeq 0$ and $\mathrm{Re}\,ω\simeq 0$, can be justified from the Monte-Carlo configurations sampled on the optimized path. We also derive the Euler-Lagrange equation for the optimal path to satisfy. The two optimized paths, the solution of the Euler-Lagrange equation and the variationally optimized path, agree with each other in the region with large statistical weight.

hep-lat↗

arXiv2019

Phase transition encoded in neural network

We discuss an aspect of neural networks for the purpose of phase transition detection. To this end, we first train the neural network by feeding Ising/Potts configurations with labels of temperature so that it can predict the temperature of input. We do not explicitly supervise whether the configurations are in ordered/disordered phase. Nevertheless, we can identify the critical temperature from the parameters (weights and biases) of trained neural network. We attempt to understand how temperature-supervised neural networks capture the information of phase transition by paying attention to what quantities they learn. Our detailed analyses reveal that they learn different physical quantities depending on how well they are trained. Main observation in this study is how the weights in the trained neural-network can have information of the phase transition in addition to temperature.

cond-mat.dis-nn↗

arXiv2019

Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction

The path optimization method is applied to a QCD effective model with the Polyakov loop and the repulsive vector-type interaction at finite temperature and density to circumvent the model sign problem. We show how the path optimization method can increase the average phase factor and control the model sign problem. This is the first study which correctly treats the repulsive vector-type interaction in the QCD effective model with the Polyakov-loop via the Markov-chain Monte-Carlo approach. It is shown that the complexification of the temporal component of the gluon field and also the vector-type auxiliary field are necessary to evade the model sign problem within the standard path-integral formulation.

hep-lat↗

arXiv2019

Path optimization in 0+1 dimensional QCD at finite density

We investigate the sign problem in 0+1 dimensional QCD at finite chemical potential by using the path optimization method. The SU(3) link variable is complexified to the SL(3,$\mathbb{C}$) link variable, and the integral path is represented by a feedforward neural network. The integral path is then optimized to weaken the sign problem. The average phase factor is enhanced to be greater than 0.99 on the optimized path. Results with and without diagonalized gauge fixing are compared and proven to be consistent. This is the first step of applying the path optimization method to gauge theories.

hep-lat↗

arXiv2019

Color Superconductivity in Holographic SYM Theory

A holographic bottom-up model used in studying the superconducting system is applied to search for the color superconducting phase of supersymmetric Yang-Mills theory. We apply the probe analysis of this model to the supersymmetric Yang-Mills theory in both the confinement and deconfinement phases. In this analysis, we find the color superconductivity in both phases when the baryon chemical potential exceeds a certain critical value. This result implies that, above the critical chemical potential, a color non-singlet diquark operator, namely the Cooper pair, has its vacuum expectation value even in the confinement phase. In order to improve this peculiar situation, we proceed the analysis by taking account of the full back-reaction from the probe. As a result, the color superconducting phase, which is observed in the probe approximation, disappears in both the confinement and deconfinement phases when parameters of the theory are set within their reasonable values.

hep-th↗

arXiv2019

Roberge-Weiss periodicity, canonical sector and modified Polyakov-loop

To obtain deeper understanding of QCD properties at finite temperature, we consider the Fourier decomposition of the grand-canonical partition function based on the canonical ensemble method via the imaginary chemical potential. Expectation values are, then, represented by summation over each canonical sector. We point out that the modified Polyakov-loop can play an important role in the canonical ensemble; for example, the Polyakov-loop paradox which is known in the canonical ensemble method can be evaded by considering the quantity. In addition, based on the periodicity issue of the modified Polyakov-loop at finite imaginary chemical potential, we can construct the systematic way to compute the dual quark condensate which has strong unclearness in its foundation in the presence of dynamical quarks so far.

hep-ph↗

arXiv2018

Path optimization method with use of neural network for the sign problem in field theories

We investigate the sign problem in field theories by using the path optimization method with use of the neural network. For theories with the sign problem, integral in the complexified variable space is a promising approach to obtain a finite (non-zero) average phase factor. In the path optimization method, the imaginary part of variables are given as functions of the real part, $y_i=y_i(\{x\})$, and are optimized to enhance the average phase factor. The feedforward neural network can be used to give and to optimize functions with many variables. The combined framework, the path optimization with use of the neural network, is applied to the complex $ϕ^4$ theory at finite density, the 0+1 dimensional QCD at finite density, and the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model, all of which have the sign problem. In these cases, the average phase factor is found to be enhanced significantly. In the complex $ϕ^4$ theory, it is demonstrated that the number density is calculated at a high precision. On the optimized path, the imaginary part is found to have strong correlation with the real part on the temporal nearest neighbor site. In the 0+1 dimensional QCD, we compare the results in two different treatments of the link variable: optimization after the diagonal gauge fixing and optimization without the diagonal gauge fixing. These two methods show consistent eigenvalue distribution of the link variables. In the PNJL model with homogeneous field ansatz, finite volume results approach the mean field results as expected, and the phase transition behavior can be described.

hep-lat↗

arXiv2018

Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop

We apply the path optimization method to a QCD effective model with the Polyakov loop at finite density to circumvent the model sign problem. The Polyakov-loop extended Nambu--Jona-Lasinio model is employed as the typical QCD effective model and then the hybrid Monte-Carlo method is used to perform the path integration. To control the sign problem, the path optimization method is used with complexification of temporal gluon fields to modify the integral path in the complex space. We show that the average phase factor is well improved on the modified integral-path compared with that on the original one. This indicates that the complexification of temporal gluon fields may be enough to control the sign problem of QCD in the path optimization method.

hep-ph↗

arXiv2018

Anomalous Hall effect in dense QCD matter

In this letter, we investigate the anomalous Hall effect in dense QCD matter. When the dual chiral density wave which is the spatially modulated chiral condensate appears in the medium, it gives rise to two Weyl points to the single-particle energy-spectrum and then the anomalous Hall conductivity becomes nonzero. Then, dense QCD matter is analogous to the Weyl semimetal. The direct calculation of the Hall conductivity by way of Kubo's linear response theory gives the term proportional to the distance between the Weyl points. Unlike the Weyl semimetal, there appears the additional contribution induced by axial anomaly.

hep-ph↗

arXiv2017

Application of neural network to sign problem via path optimization method

We introduce the feedforward neural network to attack the sign problem via the path optimization method. The variables of integration is complexified and the integration path is optimized in the complexified space by minimizing the cost function which reflects the seriousness of the sign problem. For the preparation and optimization of the integral path in multi-dimensional systems, we utilize the feedforward neural network. We examine the validity and usefulness of the method in the two-dimensional complex $λϕ^4$ theory at finite chemical potential as an example of the quantum field theory having the sign problem. We show that the average phase factor is significantly enhanced after the optimization and then we can safely perform the hybrid Monte-Carlo method.

hep-lat↗